Journal of Superconductivity and Novel Magnetism

, Volume 27, Issue 1, pp 195–201

Impedance Spectroscopy Properties of Pr0.67A0.33MnO3 (A = Ba or Sr) Perovskites


    • Laboratoire de Physico-chimie des Matériaux, Département de Physique, Faculté des Sciences de MonastirUniversité de Monastir
  • S. Khadhraoui
    • Laboratoire de Physico-chimie des Matériaux, Département de Physique, Faculté des Sciences de MonastirUniversité de Monastir
  • A. Triki
    • Laboratoire des Matériaux Composites, Céramiques et Polymères, Faculté des Sciences de SfaxUniversité de Sfax
  • S. Zemni
    • Laboratoire de Physico-chimie des Matériaux, Département de Physique, Faculté des Sciences de MonastirUniversité de Monastir
  • M. Boudard
    • Laboratoire des Matériaux et du Génie Physique, Grenoble INP, CNRS (UMR 5628)MINATEC
  • M. Oumezzine
    • Laboratoire de Physico-chimie des Matériaux, Département de Physique, Faculté des Sciences de MonastirUniversité de Monastir
Original Paper

DOI: 10.1007/s10948-013-2240-2

Cite this article as:
Hcini, S., Khadhraoui, S., Triki, A. et al. J Supercond Nov Magn (2014) 27: 195. doi:10.1007/s10948-013-2240-2


We have investigated the dielectric properties of Pr0.67Ba0.33MnO3 (PBMO) and Pr0.67Sr0.33MnO3 (PSMO) perovskites synthesized by the solid-state reaction method at 1473 K. Samples were characterized by complex impedance spectroscopy (CIS) in the frequency range from 40 Hz to 1 MHz, at room temperature. The conductivity curves for the two samples were well fitted by the Jonscher law σ(ω)=σdc+n. For the PBMO sample, the hopping process occurs at long distance, whereas for PSMO compound it occurs between neighboring sites. Frequency dependence of dielectric constant (ε″) and tangent loss (tanδ) show a dispersive behavior at low frequencies that was explained on the basis of the Maxwell–Wagner model and Koop’s theory. Electric modulus formalism has been employed to study the relaxation dynamics of charge carriers. For both compounds, the variation of the imaginary part Z″ shows a peak at a relaxation angular frequency (ωr) related to the relaxation time (τ) by τ=1/ωr. Nyquist plots of impedance show the presence of two semicircles and an electrical equivalent circuit has been proposed to explain the impedance results.


PerovskitesDielectric propertiesImpedance spectroscopyGrains and grain boundaries effects

1 Introduction

Perovskite manganese oxides, Ln1−xAxMnO3 (Ln = rare earth, A= Ca, Sr, Ba, etc.) have been extensively studied in the last years due to their interesting properties, which suggest the possibility of applications in diverse technology areas. The various physical properties of these perovskites materials are highly influenced by many factors such as the method of synthesis, the doping level in the A-site [1], the average ionic radius of A-site [2], the deficiency of oxygen [3], grains and grain boundaries effects [4, 5], etc. These materials are interesting in the electrochemical applications such as air electrodes in solid oxide fuel cells (SOFC) [6], in the magnetic refrigeration applications [7, 8], and in electronic technologies such as magnetic recording at high density and high-sensitivity magnetic sensors [9, 10].

A way to control the dielectric properties of perovskites materials can be achieved by the complex impedance spectroscopy (CIS). Along this line, several studies have been reported in the literature in order to understand the nature of electrical conduction process in these materials [1113].

Recently, we have studied the structure, and the magnetic and electrical properties of Pr0.67Ba0.33MnO3 (PBMO)1 and Pr0.67Sr0.33MnO3 (PSMO) perovskites [5]. Both compounds exhibit a transition from a paramagnetic-insulator (PMI) to a ferromagnetic-metallic (FMM) states. We have also shown in our recent work [14], using the percolation model that the observed metal-insulator (M-I) transition in our samples can be due to a percolation of FMM domains.

The objective of the present work is to compare the dielectric and ac-conduction properties of PBMO and PSMO compounds over the wide range of frequencies at room temperature. Conductivity, dielectric, and complex impedance properties of our materials can be determined and interpreted from the CIS, which is an important and powerful technique to study the dielectric and conduction properties of materials.

2 Experimental

Polycrystalline samples were prepared using solid-state reaction at 1473 K. Microstructure analysis, M(T) and ρ(T) measurements were reported in our previous work [5]. The dielectric properties were examined by an impedance analyzer (Novocontrol Alpha-analyzer) over a broad frequency range (40 Hz–1 MHz) at room temperature. In the impedance analyzer, the sintered disk with a diameter of 10 mm and a thickness of approximately 2 mm was placed between two gold parallel electrodes.

The real (ε′) and imaginary (ε″) parts of the permittivity were calculated from the impedance data using the relation:
$$ \varepsilon^{*} = \varepsilon'-i\varepsilon'' = \frac{1}{i\omega C_{0}Z^{*}}, $$
where Z is the complex impedance, ω=2πf is the angular frequency with f the frequency of the applied field, \(C_{0}= \frac{\varepsilon _{0}S}{d}\) is the empty cell capacitance with ε0 the permittivity of free space (ε0=8.854×10−12 F/m), d is the sample thickness, and S is the area of the sample.
The electrical conductivity σ for our samples was calculated using the following relation:
$$ \sigma = \omega \varepsilon_{0} \varepsilon'' $$
The loss factor tangent (tanδ) was calculated using the relation:
$$ \tan \delta = \frac{\varepsilon''}{\varepsilon'} = \frac{Z'}{Z''} $$
Electrical modulus analysis is given by the following equations:
$$ M^{*} = 1/\varepsilon^{*} = M' + jM'' $$
$$\begin{aligned} &{M' = \varepsilon'/(\varepsilon'^{2} + \varepsilon^{\prime\prime 2})} \end{aligned}$$
$$\begin{aligned} &{M'' = \varepsilon''/(\varepsilon^{\prime 2} + \varepsilon^{\prime\prime 2})} \end{aligned}$$

3 Electrical Conductivity Studies

Figure 1 shows the semilog plot of conductivity σ at room temperature with frequency. The study of the frequency dependence of the conductivity is a well-established method for characterizing the hopping dynamics of the charge carrier.
Fig. 1

Variation, at room temperature, of the conductivity, σ, vs. frequency for PBMO and PSMO samples. Green solid line represents the fitting to the experimental data using the universal Jonscher power law σ(ω)=σdc+n (Color figure online)

The conductivity plot exhibits both low and high frequency dispersion phenomena [1517]. The low-frequency region (as shown by a plateau in Fig. 1) corresponds to the dc conductivity (σdc), which is due to the band conduction, and it is frequency independent. The high-frequency region corresponds to the ac conductivity (σac), which is attributed to the dielectric relaxation caused by the localized electric charge carriers, and it is frequency dependant.
  1. (i)
    In the plateau region, the conductivity (σdc) is higher for PSMO than that for PBMO as clearly shown in Fig. 1 and their values are compared in Table 1. This result indicates that the conduction process is more activated for PSMO than that for PBMO. This difference in σdc for the two compounds may be related to the prominent role of the grain boundary in PBMO which decreases the double exchange coupling (DEC) of Mn3+–O2−–Mn4+ and in turn makes the PBMO sample lesser conductor as compared with PSMO [5].
    Table 1

    The best fitting parameters obtained from experimental data of the conductivity as a function of frequency using the Jonscher power law σ(ω)=σdc+n


    Sample code















  2. (ii)
    In Fig. 1, the variation of (σac) at high frequencies (ω>105 Hz) occurs with changes in the slope and can be described by the power law [1517]:
    $$ \sigma_{ac}(\omega) = A\omega^{n}, $$
    where A is the preexponential factor and n is the power law exponent. The exponent n represents the degree of interaction between mobile ions with the lattice and the coefficient A determines the strength of polarizability.
To conclude, the electrical conductivity σ for our samples follows the Jonscher power law [1820]:
$$ \sigma(\omega) = \sigma_{dc} + \sigma_{ac} = \sigma_{dc} + A\omega^{n} $$
According to Funke [21], the value of n has a physical meaning. n≤1 means that the hopping motion involves a translational motion with a sudden hopping whereas n>1 means that the motion involves localized hopping without the species leaving the neighbors.

Equation (7) is used to fit the conductivity data for PBMO and PSMO samples. In the fitting procedure, the A and n values have been varied simultaneously to get the best fits. One can see that the fitting was perfectly matched with the measured values. The representative nonlinear fitting curves and the calculated values are given in Fig. 1 and Table 1, respectively. The goodness of fit is usually evaluated by comparing the squared coefficient of linear correlation coefficient (R2) (see Table 1).

We find that the obtained value of n for PBMO sample is inferior to 1, which corresponds to a hopping process through long distance, whereas for the PSMO sample, n is superior to 1. This indicates that the hopping occurs between neighboring sites (see the schematic representation by more condensed arrows in Fig. 2b than in Fig. 2a, which presents more of porosity).
Fig. 2

A schematic representation by arrows for comparison of the hopping process: (a) through long distance for PBMO; (b) between neighboring sites for PSMO illustrated by morphology of grains given by SEM micrographs taken from our previous work [5]

4 Dielectric Studies

Figure 3a and b illustrate the frequency dependence at room temperature of dielectric constant (ε″) and dielectric loss (tanδ), respectively, for PBMO and PSMO samples. For both compounds, the dielectric constant exhibits larger dispersion at low frequencies while it decreases to a constant value at higher frequencies (in the range 103–106 Hz). This behavior is well explained by the Maxwell–Wagner type relaxation, often occurring in the heterogeneous systems [22]. When an electric current passes through interfaces between two different dielectric media, because of their different conductivities, surface charges pile up at the interfaces giving rise to interfacial polarization at the boundaries. These space charges align with the applied electric field at lower frequencies but as frequency increases the dipoles cannot synchronize with the frequency of the applied field so their contribution is reduced, giving rise to low dielectric constant. According to this model the sample consists of perfectly conducting grains separated by insulating grain boundaries. The Koop’s phenomenological theory postulates that grain boundaries are effective at low frequencies and grains are effective at high frequencies [23]. This is consistent with the lower value of ε″ for PBMO than that for PSMO, indeed PBMO presents more of porosity, and hence higher grain boundaries effects (compare Fig. 2a and b). At higher frequencies, the polarization decreases with increasing frequency and reaches a constant value which leads to a decrease in dielectric constant for both compounds.
Fig. 3

Frequency dependence of (a) imaginary part of dielectric permittivity and (b) loss factor tangent for PBMO and PSMO samples at room temperature

Due to higher resistance offered by the grain boundaries at low frequencies more energy is required for the motion of charge carriers, and hence the energy loss (tanδ) is also high in this frequency range (see Fig. 3b). On the other hand, at high frequencies as low resistance is offered by grains less energy is required by the charge carriers for motion so the dielectric loss is low.

5 Electrical Modulus Analysis

Figure 4a shows the variation of the real part of the electrical modulus M′ with frequency at room temperature. We can note a very low M′ value (close to zero) in the low frequency region and then an increase when the frequency approaches ultimately the M value. This may be attributed to the conduction phenomena due to short-range mobility of charge carriers.
Fig. 4

Frequency dependence of real and imaginary parts of dielectric modulus M: (a) for M′ and (b) for M″ for the two samples PBMO and PSMO at room temperature

The variations of imaginary part of electrical modulus M″ with frequency at room temperature are shown in Fig. 4b from which we can note that the position of the relaxation peaks shift toward higher frequencies from PBMO to PSMO, thus providing means for the study of relaxation. Consequently, this means that relaxation rate for this process increases from PBMO to PSMO. The low-frequency side of the imaginary part of modulus determines the range in which charge carriers are mobile on long distances (the charge carriers represent the possibility of the ion migration via hopping from one site to the neighboring site). At high frequency, above the peak (maximum of M″), the carriers are spatially confined to potential wells, being mobile on short distances, and thus could be made to have localized motion within the well.

The broadening of the peak suggests the spread of relaxation time with different time constants, which indicates that is nonexponential and this profile corresponds to a non-Debye relaxation. This is consistent with the impedance data (see Sect. 6). The electric modulus M represents the real dielectric relaxation process and should be replaced by a frequency-dependent electric modulus which can be expressed by the following equation [2426]:
$$ M = M_{\infty} \biggl[ 1 - \int_{0}^{\infty} \biggl( - \frac{d\phi (t)}{dt}\biggr) \exp(- jwt)\,dt\biggr] $$
where M=1/ε is the asymptotic value of M′(ω) and ϕ(t)=exp[−(t/τM)β] represents the time evolution of the electric field within the material, where (0<β<1) is the stretched exponent and τM is the conductivity relaxation time.

6 Complex Impedance Analysis

Figure 5a shows the variation of the real part (Z′) of the complex impedance, Z, as a function of frequency ω, at room temperature, for PBMO and PSMO samples. It is clear from these curves that the values of Z′ are found to decrease with increasing ω, which indicates an increase in the ac conductivity. These curves reveal that the PSMO sample presents the lowest real part Z′, which shows higher conductivity in comparison with the PBMO sample. This is in perfect agreement with the interpretation of previous conductivity results.
Fig. 5

Variation, at room temperature, of the real (a) and imaginary (b) parts of the complex impedance Z as a function of frequency for PBMO and PSMO samples

The merge in curves of Z′ in the higher frequency region for the two samples is probably due to the release of space charges as a result of reduction in the barrier properties of the material at room temperature and can be interpreted by the presence of space charge polarization.

The plot of imaginary part of the impedance (Z″), at room temperature, for PBMO and PSMO compounds is shown in Fig. 5b. Both spectra are characterized by the appearance of peaks which shift to higher frequencies for PSMO. Such behavior indicates the presence of relaxation in our compounds [27, 28]. Peak position on frequency axis gives the relaxation frequency (ωr)2 and the relaxation time (τ)3 using the following relation:
$$ \tau = 1/\omega_{r} $$
The complex impedance spectrum gives the direct correlation between the response of a real system and an idealized model circuit composed of discrete electrical components. The variation of Z″ vs. Z′ for the two samples are represented as Nyquist plots in Fig. 6. This impedance representation is characterized by the appearance of semicircle arcs not centered on the real axis. Such decentralization is an indicative of non-Debye type relaxation process and PSMO and PBMO obey to the Cole–Cole formalism [22, 29].
Fig. 6

Complex impedance spectrum (Nyquist plot) of PBMO and PSMO samples at room temperature with electrical equivalent circuit

The impedance data are fitted using Zview software and the best fit (green solid line in Fig. 6) is obtained when employing an equivalent circuit formed by a resistance R1 (grain resistance Rg) in series with a parallel combination of resistance R2 (grain boundary resistance Rgb) and constant phase element impedance (ZCPE). The equivalent configuration is of the type [R1+(R2//ZCPE)], as shown in the inset of Fig. 6.

The CPE impedance (ZCPE) is given by the following relation [3032]:
$$ Z_{\mathrm{CPE}} = \frac{1}{T(j\omega)^{p}} $$
where T (F sp−1 or Ω−1 s) is the CPE parameter, \(j=\sqrt{-1}\) and p the CPE exponent (0≤p≤1).
According to P. Zoltowski [33] and Z. Stoynov et al. [34], the CPE is identical to:
  1. (i)

    capacitance when p=1.

  2. (ii)

    warburg impedance when p=0.5.

  3. (iii)

    simple resistance when p=0.

The impedance can be expressed in terms of a CPE as
$$ Z(\omega) = R_{1} + \frac{R_{2}}{1+TR_{2}(j\omega)^{p}} $$
In Table 2, we give the parameters (R1,R2,T, and p) obtained after fitting the data of our samples. It is clear that the value of grain resistance R1 is significantly lower for PSMO than for PBMO, which can be explained by the increase of the mobility of charge carriers for PSMO than for PBMO. This confirmed that PSMO is more conductive than PBMO.
Table 2

Electrical parameters of equivalent electrical circuit deduced from complex impedance spectrum for PBMO and PSMO samples

Sample code

R1=Rg (kΩ)

R2=Rgb (kΩ)

T (nF)












Table 2 shows also that the grain boundary resistance R2, is lower for PSMO than for PBMO. It seems to be due to the fact that the grain boundary effect has assisted in lowering the barrier to the motion of charge carriers paving the way for increased electrical transport with rise in temperature.4 The evidences of grain boundary conduction have been observed in perovskites ceramic, ceramic conductors, and also in ceramic dispersed ionically conducting composite polymers [3537].

7 Conclusion

We have investigated in this work the dielectric properties of PSMO and PBMO samples using complex impedance spectroscopy at room temperature. Electrical conductivity curves are found to obey Jonscher universal power law. The hopping process occurs at long distance for PBMO sample and between neighboring sites for PSMO compound. Frequency dependence of dielectric constant (ε″) and tangent loss (tanδ) at room temperature indicate a dispersive behavior at low frequencies. The relaxation dynamics of charge carriers for our samples has been studied using the modulus spectra. Complex impedance analysis indicates that the dielectric properties of the materials are strongly dependent on frequency and can be described as grains and grain boundary media. Impedance spectrum is characterized by the appearance of semicircle arcs which are well modeled in terms of electrical equivalent circuit with a grain resistance (Rg) in series with a parallel combination of grain boundary resistance (Rgb) and constant phase element impedance (ZCPE). The values of Rg and Rgb are lower for PSMO than for PBMO which confirms that PSMO is more conductive than PBMO.


We use the abbreviations (PBMO) and (PSMO).


ωr=20257.21 Hz for PBMO and ωr=25302.87 Hz for PSMO.


τ=4.94×10−5 s for PBMO and τ=3.99×10−4 s for PSMO.


Our measurements were made at room temperature (i.e., at sufficiently high temperature).


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© Springer Science+Business Media New York 2013